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Консультация № 197437
15.12.2019, 05:20
0.00 руб.
20.12.2019, 02:34
0
1
1
Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
С помощью перехода к полярным координатам вычислить двойной интеграл:
С помощью перехода к полярным координатам вычислить двойной интеграл:
Обсуждение
20.12.2019, 03:10
общий
это ответ
Здравствуйте, Smurf!
Переход к полярным координатам осуществляется по формулам: x = r cos [$966$], y = r sin [$966$], dx dy = r dr d[$966$]. Тогда область интегрирования запишется как D = {r[sup]2[/sup][$8804$]1, r cos [$966$][$8805$]0, r sin [$966$][$8805$]0} = {0[$8804$]r[$8804$]1, 0[$8804$][$966$][$8804$][$960$]/2}, а интеграл примет вид
Внутренний интеграл равен
тогда
Переход к полярным координатам осуществляется по формулам: x = r cos [$966$], y = r sin [$966$], dx dy = r dr d[$966$]. Тогда область интегрирования запишется как D = {r[sup]2[/sup][$8804$]1, r cos [$966$][$8805$]0, r sin [$966$][$8805$]0} = {0[$8804$]r[$8804$]1, 0[$8804$][$966$][$8804$][$960$]/2}, а интеграл примет вид
Внутренний интеграл равен
тогда
Форма ответа
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